Abstract
We prove that all bounded weak solutions of the fourth order system 2u D Q.x; u;ru/; u 2 W 2;2; where the nonlinearity grows critically with the gradient of a solution, i.e., jQ.x; u;ru/j . jruj4, are regular once an appropriate smallness condition (expressed in terms of Morrey norms and guaranteeing that u is small in BMO) is satisfied. The result holds in every dimension.
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